[Extrarius]

For money, I see two easy options that haven't been mentioned:

First, the market could work on a credit system with there being a yearly/seasonal 'settlement week/day/etc' where people pay their credit in multiple ways (decided at time of writing the 'IOU') - commodities (grains, seasonings, etc), other staple foods (preserved meats, jarred fruit preserves), and, occasionally, actually currency. My understanding is that Japan worked something like this for a while, at least for expensive items (perhaps only for items that required commissioning).

Second, there could be a common magic item akin to "The Bag of Holding" that comes in many sizes, such that a fairy would have a tiny bag with the opening just big enough to fit a coin through and a titan might own a bag whose opening could be big enough to easily place people of any other race, carts, horses, etc in the bag. This still leaves the problem that the titan will have difficulty counting out tiny coins. One nice way to solve this would be to mimic an ability from the "Handy Haversack", which effectively helps you grab the contents you want - the titan imagines which coins they want, reaches in, and finds those coins in his hand without having to tediously feel around for the minuscule coins. Another option would be to let the magic bag merge coins into bars and vice versa.
If you don't want magic items everywhere, perhaps the city itself has some kind of system that provides the magic (obelisks evenly distributed around town, perhaps), so the bags only function in the city (and if taken outside the city, the contents stays in the pocket dimension inside the city, and you just have an empty bag with some runes/sigils/etc on it).

Thinking more about feudal Japan, if the coins were slightly on the large side with holes through the center, titans could more easily handle groups of coins strung together, and they're going to need larger sums for most things anyways, so that might help some. If they need to make strings of a certain value, though, it'd be a very tedious process for the titans (almost certainly involving something like a beading needle). I've used very tiny beads that are smaller than 1/10th the size of a modern coin, and it was a pain, but doable (with improvised equipment - had to find a very tiny sewing needle and dull the edge a bit to make a beading needle that'd fit through the beads).